Single domain globular proteins containing less than 100 residues often show simple thermodynamic and kinetic properties with only two populations of molecules (folded and unfolded) present at all times and under all solution conditions1. Two-state behavior is characterized by a linear relation between the apparent activation free energy changes and the concentration of chemical denaturant, resulting in a V-shaped plot of the log(relaxation rate) vs denaturant concentration, called a chevron plot. For a two-state system the relaxation rate is the sum of the folding and unfolding rates and the equilibrium constant is the ratio. The most common chevron plot has linear arms at low and high denaturant concentrations where the relaxation rate corresponds to the folding and unfolding rates, respectively. As in the linear free energy relations observed in chemical reactions, the relative sensitivity of the folding and unfolding rates resulting from the change in stability is taken as a measure of the position of the transition state along a putative reaction coordinate, in this case the compactness of the structure. There has been much discussion on the interpretation and significance of deviations from linear folding and unfolding arms to the chevron plots. Several factors have been suggested as causes for this deviation, including the presence of intermediate states, a change in the relative position of the transition and denatured states with changing solvent conditions or mutation, and the presence of parallel pathways. Most recently, the magnitude of the slopes of the chevron plots were used by Muoz and coworkers to make quantitative estimates of the free energy barrier height separating folded and unfolded states for fast-folding proteins. Using an idealized free energy surface they concluded that the lack of denaturant dependence in the relaxation rate is a signature of barrierless folding. Fersht and coworkers also suggested that there would be little denaturant dependence if there is no barrier separating folded and unfolded states.[unreadable] [unreadable] We have addressed the connection between free energy surfaces and chevron plots in a kinetic study of a small very-fast folding protein, the 35-residue subdomain from the villin headpiece.The denaturant-induced unfolding curves, measured by circular dichroism and fluorescence, are typical for small single domain proteins and are well fit assuming a two-state thermodynamic model. The kinetics, however, are strikingly different from what is observed for slower folding two-state proteins, with no measurable dependence of the relaxation rate on denaturant concentration.[unreadable] [unreadable] To understand the denaturant-independent relaxation rates, we have used an Ising-like model as a guide. The kinetics of folding and unfolding are calculated by hopping along the one-dimensional free energy surface generated from the partition function (Fig. 3), with the fraction of native contacts or number of ordered residues as a reaction coordinate. The model clewarly shows that a nearly denaturant-invariant, unfolding/refolding relaxation rate can be produced by a large movement of the major free energy barrier, together with a denaturant- and reaction coordinate-dependent diffusion coefficient. Although barrierless folding might result in little or no denaturant dependence, the converse is not necessarily true.